Interesting features of transmission across locally periodic delta potentials

Dharani, M.; Shastry, C. S.

doi:10.1063/1.4948038

Cited by 2 publications

(7 citation statements)

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“…Energy gap zones are no longer forbidden. Still, oscillatory transmission behaviors as function of energy seem to be localized to 'transmission bands' [10]. Such bands are in this study confirmed being closely related to Floquet/Bloch energy band zones as the number of period cells is large.…”

supporting

confidence: 78%

“…It is also confirmed that multi-well potentials may cause an incomplete transmission band near the threshold energy [9,10].…”

mentioning

confidence: 84%

“…where = d / d x. Due to the relation (10), the Wronskian determinant of the two solutions ( 9) is independent of x [24].…”

Section: General Amplitude-phase Approachesmentioning

confidence: 99%

“…where the value u p is so far unspecified. The phase p p (x) is related to A p (x) as given in (10).…”

Section: Approach Using Intrinsic Floquet/bloch Quantitiesmentioning

confidence: 99%

“…A limitation is possibly the lack of realistic interactions studied. Potentials are usually constructed by delta functions and/or square well/barrier functions of the space coordinate [7,10,11]. Novel aspects of non-uniform lattice potentials constructed by various rectangular potential pieces are discussed by Das (2015) [13].…”

mentioning

confidence: 99%

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Quantum transmission for embedded, locally periodic potentials -- amplitude-phase approaches

Thylwe

2020

Preprint

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Quantum particle transmission through locally periodic potentials surrounded by symmetric exterior potentials is analyzed. Closed-form conditions for locating energy peaks of total transmission are derived. Floquet/Bloch energy band types are defined and found to affect the number of peaks in transmission bands. Modifications of band types and a band fusion phenomenon are discussed.The theoretical approaches suggested consist of several ways to express a Schrödinger wave as an amplitude function multiplying a harmonic function of a phase function. In particular, an approach containing a Floquet/Bloch periodic amplitude function and a corresponding phase function is described for the locally periodic region, allowing a way to specify quantum numbers for energies of total transmission. I. INTRODUCTIONOne-dimensional quantum scattering caused by locally periodic potentials introduce useful theoretical notions like Floquet/Bloch energy bands and gaps, which are helpful for understanding more complicated physical systems. Chemical selections of gas components [1, 2] is one application. For example mass selections, where total transmission is monitored for a certain mass and minimal transmission for a slightly different mass. Manipulation of electronic properties of material structures such as graphene [3]-[6] is another of many applications. An introductory review is given by Griffiths and Steinke (2001) [7]. The authors cover examples related to several mechanical systems: transverse waves on weighted strings, longitudinal waves on weighted rods, acoustic waves in corrugated tubes, and water waves crossing a sequence of sandbars. The authors also discuss electromagnetic waves in transmission lines and photonic crystals, as well as relativistic quantum scattering described by the Dirac equation in one space dimension. The so-called 'transfer matrix' method [7-9] is applied in most published numerical studies. A limitation is possibly the lack of realistic interactions studied. Potentials are usually constructed by delta functions and/or square well/barrier functions of the space coordinate [7,10,11]. Novel aspects of non-uniform lattice potentials constructed by various rectangular potential pieces are discussed by Das (2015) [13]. In the present study the locally periodic part of the potentials are uniform and smooth. Non-smooth potentials cannot easily be generalized to second-order Dirac equations for analysing relativistic effects [12]. Floquet theory is focusing on time-periodic systems of ordinary differential equations [14][15][16][17]. It applies to spaceperiodic quantum systems as well, and is an alternative to Bloch's theory of space-periodic material structures.Behaviors of quantum particles in a locally periodic potential are related to behaviors of typical (time-periodic) Floquet solutions: appearances of continuous intervals of forbidden energies defining energy gaps (exponentially

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supporting

confidence: 78%

“…It is also confirmed that multi-well potentials may cause an incomplete transmission band near the threshold energy [9,10].…”

mentioning

confidence: 84%

“…where = d / d x. Due to the relation (10), the Wronskian determinant of the two solutions ( 9) is independent of x [24].…”

Section: General Amplitude-phase Approachesmentioning

confidence: 99%

“…where the value u p is so far unspecified. The phase p p (x) is related to A p (x) as given in (10).…”

Section: Approach Using Intrinsic Floquet/bloch Quantitiesmentioning

confidence: 99%

mentioning

confidence: 99%

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Quantum transmission for embedded, locally periodic potentials -- amplitude-phase approaches

Thylwe

2020

Preprint

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Model study of transmission across N periodically placed ionic molecules in one dimension

Dharani¹,

Shastry²

2017

AIP Conference Proceedings

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Interesting features of transmission across locally periodic delta potentials

Cited by 2 publications

References 4 publications

Quantum transmission for embedded, locally periodic potentials -- amplitude-phase approaches

Quantum transmission for embedded, locally periodic potentials -- amplitude-phase approaches

Model study of transmission across N periodically placed ionic molecules in one dimension

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